Question

The initial rate of hydrolysis methyl acetate ($1M$) by a weak acid ($HA,1M$) is $1/{100}^{th}$ of that of a strong acid ($HX,1M$), at ${25}^{o}C$. The $K_a$of $HA$ is:

• A. 1 x 10${}^{-4}$
• B. 1 x 10${}^{-5}$
• C. 1 x 10${}^{-6}$
• D. 1 x 10${}^{-3}$

Answer 1

The correct option is A 1 x 10${}^{-4}$

The rate of the hydrolysis of methyl acetate is directly proportional to the hydrogen ion concentration.
In case of weak acid, the equilibrium constant is given by the expression $K_a=\frac{\left[H^{+}\right]\left[A^{-}\right]}{\left[HA\right]}=\frac{[H^{+}{]}^2}{\left[HA\right]}$
Hence, $\left[H^{+}\right]=\sqrt{K_a\left[HA\right]}$

Hence, the expression for the ratio of the rate of the hydrolysis of methyl acetate in presence of weak acid and strong acid becomes $\frac{r_{weakacid}}{r_{strongacid}}=\frac{\sqrt{K_a\left[HA\right]}}{\left[HA\right]}=\frac{1}{100}$

Substitute $\left[HA\right]=1M$

Hence, $\frac{\sqrt{K_a\times 1}}{1}=\frac{1}{100}$
$K_a=1\times {10}^{-4}$